Limiting absorption principle for the electromagnetic Helmholtz equation with singular potentials

2011/04/21 by Zubeldia, Miren · 1 citation
#35J05 #35J10 #35J15 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1104.4237

Abstract

We study the following Helmholtz equation (∇ +iA(x))² u+ V₁(x) u + V₂(x) u + λu = f(x) in ℝ^d with magnetic and electric potentials that are singular at the origin and decay at infinity. We prove the existence of a unique solution satisfying a suitable Sommerfeld radiation condition, together with some a priori estimates. We use the limiting absorption method and a multiplier technique of Morawetz type.

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• Sampling and equidistribution theorems for elliptic second order operators, lifting of eigenvalues, and applications

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